Methods and systems for sampling frequency offset detection, correction and control for MIMO OFDM systems

ABSTRACT

Methods and systems that are capable of detecting and correcting the sampling frequency offset as part of signal synchronization in MIMO OFDM systems. An exemplary MIMO OFDM system includes a transmitter with a number of OFDM modulators that provide data to antennas for transmission across a channel to a receiver. The OFDM modulators include a training symbol inserter that may insert a matrix of pilot tones into the data. The data including the matrix of pilot tones is received by a receiver having a number of OFDM demodulators including a synchronization circuit. The synchronization circuit uses the matrix of pilot tones to detect and correct the sampling frequency offset as part of the signal synchronization. The synchronization circuit may apply an open loop process including sampling frequency offset estimation, phase rotation, and channel estimation. Alternatively, the synchronization circuit may apply a closed loop process including error generation, loop filtering and accumulation as well as sampling frequency offset estimation, phase rotation, and channel estimation.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims priority to and benefit of theprior filed co-pending and commonly owned provisional application, filedin the United States Patent and Trademark Office on Oct. 4, 2002,assigned Application No. 60/416,381, and incorporated herein byreference.

FIELD OF THE INVENTIONS

[0002] The inventions relate generally to wireless communication systemsthat employ Orthogonal Frequency Division Multiplexing (OFDM). Moreparticularly, the inventions are related to systems and methods fordetecting, correcting, and controlling the sampling frequency offset ina Multi-Input, Multi-Output (MIMO) OFDM system.

BACKGROUND OF THE INVENTIONS

[0003] In wireless communication systems, a signal may be sent at acertain frequency within specified parameters, in what is called atransmission path. Recent developments have enabled the simultaneoustransmission of multiple signals over a single transmission path. One ofthese methods of simultaneous transmission is referred to as FrequencyDivision Multiplexing (FDM). In FDM, the transmission path is dividedinto sub-channels. Information (e.g. voice, video, audio, text, data,etc.) is modulated and transmitted over the sub-channels at differentsub-carrier frequencies.

[0004] A particular type of FDM is Orthogonal Frequency DivisionMultiplexing (OFDM). In OFDM technology, the sub-carrier frequencies arespaced apart by precise frequency differences. An advantage of OFDMtechnology is that it is generally able to overcome multiple patheffects. Another advantage of OFDM technology is that it is typicallyable to transmit and receive large amounts of information. A furtheradvantage is that by using multiple transmitting antennas and multiplereceiving antennas in an OFDM system, it is possible to increase thecapacity of transmitted and received data while generally using the sameamount of bandwidth as in a system with one transmitting and onereceiving antenna. Because of these advantages, much research has beenperformed to advance OFDM technology.

[0005] OFDM technology is typically divided into two categories:Single-Input, Single-Output (SISO); and Multi-Input, Multi-Output(MIMO). SISO utilizes a single transmitting antenna to transmit signalsand a single receiving antenna to receive the signals. MIMO usesmultiple transmitting antennas and multiple receiving antennas.

[0006] In typical communication systems, a preamble, at the beginning ofeach data transmission, is usually added as a prefix to the datasymbols. The data symbols, of course, include the useful data orinformation (e.g., voice, data, video, etc.), which is meant to betransmitted to a remote location. The preamble is used to provideinformation such as frequency tuning, synchronization, and channelparameter estimation. The receiver for an OFDM system in the acquisitionmode uses the information in the preamble to perform timesynchronization, frequency offset estimation and correction, and channelestimation. Sampling frequency offset may create Inter CarrierInterference (ICI), phase rotation, amplitude distortion and loss insynchronization.

[0007] Data in the preamble presents a sampling frequency, which is usedto determine if there is a frequency offset between the transmitter andthe receiver. The sampling frequency is offset in almost all systems.The transmitter and receiver each have digital clocks with oscillatorsand those can never be exactly synchronized. The effect of the offsetgets worse over time.

[0008] A receiving system can monitor and adjust the sampling frequencyin one of two ways: using an open loop system or a closed loop system.An open loop system reads the sampling frequency, monitors the offset,and performs appropriate phase rotations and timing adjustment, as thesignal passes through the receiver. A closed loop system generates anerror signal proportional to the sampling frequency offset, and performsappropriate phase rotations and timing adjustments.

[0009] An open loop system is adequate for indoor wireless or fixedwireless applications. But certain signals, such as broadcast signalssuch as streaming video, change over time and typically need to becontinuously monitored. These signals require a closed loop system.

[0010] Both open loop and closed loop systems exist for SISO OFDMsystems. However, for MIMO OFDM systems, so far as is known, neitheropen loop nor a closed loop system exists for monitoring and adjustingthe sampling frequency offset. In fact, no method or system is known toexist for a MIMO OFDM system that is capable of providing corrections tothe sampling frequency offset as part of the signal synchronization.

[0011] Accordingly, there is a need for a method or system that iscapable of detecting, correcting, and controlling the sampling frequencyoffset as part of signal synchronization in a MIMO OFDM system.

SUMMARY OF THE INVENTIONS

[0012] The inventions provide methods and systems that overcome thedeficiencies of the prior art and satisfy the need mentioned in thebackground. Advantageously, the inventions relate to methods and systemsthat are capable of detecting and correcting the sampling frequencyoffset as part of signal synchronization in MIMO OFDM systems.

[0013] An exemplary MIMO OFDM system includes a transmitter with anumber of OFDM modulators that provide data to antennas for transmissionacross a channel to a receiver. The OFDM modulators include a trainingsymbol inserter that may insert a matrix of pilot tones into the data.The data including the matrix of pilot tones is received by a receiverhaving a number of OFDM demodulators including a synchronizationcircuit. The synchronization circuit uses the matrix of pilot tones todetect and correct the sampling frequency offset as part of the signalsynchronization. The synchronization circuit may apply an open loopprocess including sampling frequency offset estimation, phase rotation,and channel estimation. Alternatively, the synchronization circuit mayapply a closed loop process including error generation, loop filteringand accumulation as well as sampling frequency offset estimation, phaserotation, and channel estimation.

[0014] Other systems, methods, features, and advantages of theinventions will become apparent to a person having skill in the art uponexamination of the following drawings and detailed description. All suchadditional systems, methods, features, and advantages are within thescope of the inventions.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015]FIG. 1 is a block diagram illustrating an exemplary embodiment ofa Multi-Input, Multi-Output (MIMO) Orthogonal Frequency DivisionMultiplexing (OFDM) system.

[0016]FIG. 2 is a block diagram illustrating an exemplary embodiment ofthe MIMO encoder shown in FIG. 1.

[0017]FIG. 3 illustrates exemplary generation of pilot tones matrix asmay be used in the inventions.

[0018]FIG. 4 illustrates an exemplary data frame structure for a MIMOOFDM system.

[0019]FIG. 5 is a block diagram illustrating an exemplary embodiment ofone of the OFDM demodulators shown in FIG. 1.

[0020]FIG. 6 is a block diagram illustrating an exemplary embodiment ofthe synchronization circuit shown in FIG. 5.

DETAILED DESCRIPTION

[0021]FIG. 1 illustrates an exemplary embodiment of a Multi-Input,Multi-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM)system 6 according to the inventions. The MIMO OFDM system 6 may beimplemented as a wireless system for the transmission and reception ofdata across a wireless channel 19. The MIMO OFDM system 6, for example,may be part of a wireless Local Area Network (LAN) system or wirelessMetropolitan Area Network (MAN) system, cellular telephone system, orother type of radio or microwave frequency system incorporating eitherone-way or two-way communication over a range of distances.

[0022] It is also possible for the exemplary MIMO OFDM system 6illustrated in FIG. 1 to be used in a system that includes an array ofsub-channel communication links that carry a number of signalstransmitted by a number of transmitting elements to each of a number ofreceiving elements. In this case, communication links, such as wires ina wiring harness or some alternative wired transmission system, forexample, could be used over the distance between a data source and areceiver.

[0023] In the exemplary MIMO OFDM system 6 of FIG. 1, a transmitter 8transmits signals across the wireless channel 19, and a receiver 10receives the transmitted signals. The transmitter 8 includes a datasource 12, which provides the original binary data to be transmittedfrom the transmitter 8. The data source 12 may provide any type of data,such as, for example, voice, video, audio, text, etc. The data source 12applies the data to an encoder 14, which encodes the data to allow forerror correction. The encoder 14 further processes the data so thatcertain criteria for space-time processing and OFDM are satisfied. Theencoder 14 separates the data onto multiple paths in the transmitter 8,each of which will hereinafter be referred to as a transmit diversitybranch (TDB). The separate TDBs are input respectively into OFDMmodulators 16, each of which modulates the signal on the respective TDBfor transmission by transmitting antennas 18.

[0024] Advantageously, the exemplary embodiment illustrated in FIG. 1may be used in a Single-Input, Single Output (SISO) system, which may beconsidered a special case of MIMO wherein the number of transmitting andreceiving antennas is, respectively, one. In the SISO system example,separation of the data by the encoder 14 is unnecessary since only oneset of an OFDM modulator 16 and an antenna 18 is used.

[0025] Reference is again made to the exemplary MIMO OFDM system 6illustrated in FIG. 1. During the encoding by the encoder 14 andmodulating by the OFDM modulators 16, data is normally bundled intogroups such that the collection of each group of data is referred to asa “frame.” Details of a frame as used in the inventions is describedbelow with reference to FIG. 5. Each frame along each TDB is output froma respective OFDM modulator 16. As illustrated in FIG. 1, any number ofOFDM modulators 16 may be used. The number of OFDM modulators 16 andrespective transmitting antennas 18 may be represented by a variable“Q.” The OFDM modulators 16 modulate the respective frames at specificsub-carrier frequencies and respective transmitting antennas 18 transmitthe modulated frames over the channel 19.

[0026] As noted in the exemplary MIMO OFDM system 6 of FIG. 1, areceiver 10 receives the transmitted signals from the transmitter 8. Inparticular, on the receiver side of the MIMO OFDM system 6, a number “L”of receiving antennas 20 receive the transmitted signals, which aredemodulated by a number L of respective OFDM demodulators 22. The numberL may represent any number and is not necessarily the same as the numberQ. In other words, the number Q of transmitting antennas 18 may bedifferent from the number L of receiving antennas 20, or they mayalternatively be the same. The outputs of the demodulators 22 are inputinto a decoder 24, which combines and decodes the demodulated signalsinto data. The decoder 24 outputs the data, which may be received by adevice (not shown) that uses the data.

[0027] The MIMO OFDM system 6 may include one or more processors,configured as hardware for executing software, particularly softwarestored in computer-readable memory. The processor can be any custom madeor commercially available processor, a central processing unit (CPU), anauxiliary processor among several processors associated with a computer,a semiconductor based microprocessor (in the form of a microchip or chipset), a macro processor, or generally any device for executing softwareinstructions.

[0028] When the MIMO OFDM system 6 is implemented in software, it may bestored on any computer-ready medium for use by or in connection with anycomputer-related system or method. A computer-readable medium is anelectronic, magnetic, optical, or other physical device or means thatcan contain or store a computer program for use by or in connection witha computer related system or method. The MIMO OFDM system 6 can beembodied in any computer-readable medium for use by or in connectionwith an instruction execution system, apparatus, or device, such as acomputer-based system, processor-containing system, or other system thatcan fetch the instructions from the instruction execution system,apparatus, or device and execute the instruction.

[0029] In an alternative embodiment, where the MIMO OFDM system 6 isimplemented in hardware, it can be implemented with any or a combinationof the following technologies, which are each well known in the art: oneor more discrete logic circuits having logic gates for implementinglogic functions upon data signals, an application specific integratedcircuit (ASIC) having an appropriate combination of logic gates, aprogrammable gate array (PGA), a field programmable gate array (FPGA),etc.

[0030]FIG. 2 illustrates details of the transmitter 8 of the exemplaryMIMO OFDM system 6 shown in FIG. 1. In particular, FIG. 2 shows detailsof an exemplary embodiment of the encoder 14 also shown in FIG. 1. Theencoder 14 may be configured such that data from the data source 12 isencoded by a channel encoder 26, which adds parity to the original datato produce channel-encoded data. The channel encoder 26 encodes the datausing a scheme that is recognized by the decoder 24 of the receiver 10and enables the decoder 24 to detect errors in the received data. Errorsmay arise as a result of environmental conditions of the channel 19 ornoise inadvertently added by the transmitter 8 or receiver 10.

[0031] The encoder 14 further includes a symbol mapper 28, whichreceives the channel-encoded data from the channel encoder 26. Thesymbol mapper 28 maps the channel-encoded data into data symbols. Thesymbol mapper 28 groups a predetermined number of bits such that eachgroup of bits constitutes a specific symbol chosen from a predeterminedalphabet. The symbol mapper 28 further lays out a stream of data symbolswithin the structure of a frame.

[0032] The encoder 14 further includes a space-time processor 30 thatreceives the data symbol stream from the symbol mapper 28. Thespace-time processor 30 processes the data symbol stream and outputs theprocessed data symbols via the respective TDBs. The space-time processor30 processes the data symbol stream in a manner such that the receiver10 of the MIMO OFDM system 6 is capable of de-processing or decoding theprocessed data symbols. The processed data symbols in the TDBs aredistributed over Q lines that will eventually be transmitted at precisefrequencies spaced apart from each other by a predetermineddifference(s) in frequency. By providing a specific frequencydifference(s) between the multiple sub-channels, orthogonality can bemaintained thereby preventing the OFDM demodulators 22 in the receiver10 of the MIMO OFDM system 6 from picking up frequencies other thantheir own designated frequency.

[0033] Each TDB provides an input to a respective adder 34. The otherinput into each of the adders 34 is connected to the output of atraining symbol inserter 32. The training symbol inserter 32 providestraining symbols to be inserted into the frames of the TDBs. Additionalinformation about the training symbol inserter 32, training symbolsincluding pilot tones, and related actions may be obtained from thecommonly owned, pending patent application entitled: “Apparatus andMethods for Providing Efficient Space-Time Structures for Preambles,Pilots and Data for Multi-Input, Multi-Output Communications Systems”,which was filed with the United States Patent and Trademark Office onSep. 17, 2002, assigned Ser. No. 10/245,090, and which is incorporatedherein by reference.

[0034] The training symbol inserter 32 may be configured so that it iscapable of storing multiple sets of training symbols. A particular setof training symbols may be selected, for example, based on desirablecommunication criteria established by a user. The training symbols foreach respective sub-channel may preferably be unique to the particularsub-channel. In order to accommodate amplitude differences between thesub-channels, the training symbols may be designed and adjusted tomaintain a constant amplitude at the output of each sub-channel.

[0035] Generally, training symbols preferably are inserted at least oncein a frame. Training symbols that are inserted at the beginning of thedata may be referred to as the preamble to the data. Nevertheless,training symbols may be inserted at other places in the data. Trainingsymbols are used for periodic calibration (synchronization and channelparameter estimation) as explained below in connection with FIG. 5. Thetraining symbols may be indicative of calibration values or known datavalues. These calibration values or known values may be transmittedacross the channel 19, and used to calibrate the MIMO OFDM system 6. Anynecessary refinements may be made to the MIMO OFDM system 6, if thereceived calibration values do not meet desirable specifications.

[0036] Further, the training symbols may be used as specific types ofcalibration values for calibrating particular channel parameters. Byinitially estimating these channel parameters, offsets in the timedomain and frequency domain may be accounted for so as to calibrate theMIMO OFDM system 6.

[0037] A particular type of training symbol referred to herein is thepilot tone. In the exemplary embodiment, as described below, pilot tonesmay be inserted into the data as part of the inventive processesrelating to sampling frequency offset detection, correction, andcontrol. Pilot tones may be inserted anywhere in the data. For example,pilot tones may be inserted periodically into the data, or scatteredthrough the data, or inserted into selected points in the data.Generally, pilot tones are used for adjustments in the signal relatingto the time-varying nature of the channel.

[0038] Per the inventions, the pilot tones are not inserted asindividual tones but as known signal transmission matrices for the MIMOconfiguration. This signal transmission matrix may be in differentforms, ranging from diagonal to unitary. However, since there is nodiversity with a diagonal matrix, an exemplary embodiment of theinventions uses an orthogonal matrix S, such as:$S_{TS} = \begin{bmatrix}{\underset{\_}{S}}_{1} & {\underset{\_}{S}}_{1} & {\underset{\_}{S}}_{1} & {\underset{\_}{S}}_{1} \\{- {\underset{\_}{S}}_{1}} & {\underset{\_}{S}}_{1} & {- {\underset{\_}{S}}_{1}} & {\underset{\_}{S}}_{1} \\{- {\underset{\_}{S}}_{1}} & {\underset{\_}{S}}_{1} & {\underset{\_}{S}}_{1} & {- {\underset{\_}{S}}_{1}} \\{- {\underset{\_}{S}}_{1}} & {- {\underset{\_}{S}}_{1}} & {\underset{\_}{S}}_{1} & {\underset{\_}{S}}_{1}\end{bmatrix}$

[0039] for an exemplary system with four transmit antennas to form thepilot tones signal transmission matrix.

[0040]FIG. 3 is a diagram of one possible system for the generation of apilot tones matrix. The pilot tones matrix is generated using a shiftregister circuit 40, as is commonly used in the art for SISO systems.The XOR gate 48 combines/compares the signals from the differentpositions of a shift register for every pilot tone within the OFDMsymbol and generates a new output which is fed to the Most SignificantBit (MSB) of the register. Initialization Sequences are normally fixedfor DownLink (DL) 43 and the UpLink (UL) 41. The DL and UL signals arearranged from Most Significant Bit (MSB) 42 to Least Significant (LSB)44. The output of the LSB is taken and a zero is mapped to a +1 voltageand a 1 is mapped to a −1 voltage. This value is then used to generatethe pilot tone matrix as shown above where the value assigned to thevariable S_(1,k) is either +1 or −1.

[0041] With reference again to FIG. 2, the adders 34 add the trainingsymbols and pilot tones to the frame. Other embodiments may be used inplace of the adders 34 for combining the training symbols (including thepilot tones) with the data symbols in the frame. Further, the adders 34may include additional inputs to allow for flexibility when adding thetraining symbols, or in the combining of multiple training symbols oreven selectable training symbols. After the training symbols areinserted into frames on the respective TDBs, the frames are output fromthe encoder 14 and input in respective OFDM modulators 16 as illustratedin FIG. 1.

[0042]FIG. 4 illustrates an example of a frame 52 that is transmittedacross the channel 19 from the transmitting antennas 18 to the receivingantennas 20. The frame 52 includes a preamble 54 and a data portion 56.The preamble 54 is inserted by the training symbol inserter 32, asmentioned above.

[0043] The preamble 54, in general, consists of Q or more trainingsymbols, wherein each training symbol has a length of G+N₁ samples intime. The number of samples N is established as a certain fraction ofthe number of data samples N in an OFDM block, such that N=N/I, where Iis an integer, such as 1, 2, 4 . . . . For example, N may be ¼(N). If nopredetermined N has been established, the variable N may be given thevalue equal to N. The training symbol length may be shorter than thelength of the symbols in the data portion 56, which has a length of G+Nsamples. The task of the preamble 54 and the training symbols N in theframe is to help the receiver 10 identify the arrival of the frame 52and perform sampling frequency offset detection, correction, andcontrol.

[0044] In addition, the frame 52 includes a data portion 56 having aplurality of OFDM data symbols N and cyclic prefixes G. The cyclicprefixes G are inserted before each of the OFDM data symbols N. Aspreviously mentioned, the training symbol inserter 32 inserts pilottones (not shown) within the OFDM data symbols N.

[0045]FIG. 5 illustrates an exemplary embodiment of one of the OFDMdemodulators 22 of the receiver 10 of the MIMO OFDM system 6. Receivedsignals from the receiving antenna 20 are input into a preamplifier 57,which amplifies the received signals to a level at which furtherprocessing may be performed. The output of the preamplifier 57 isconnected to a mixer 58. A local oscillator 59 provides a signal to themixer 58 where the signal has a frequency designed to demodulate thereceived amplified signal. The demodulated signal is then output to ananalog-to-digital converter (ADC) 60, which converts the analog signalsinto discrete time samples. The sampling frequency of the ADC may bedoubled to acquire synchronization to an accuracy of ½ the sampling timeT. The discrete time samples are applied to a synchronization circuit61, which is discussed below with reference to FIG. 6. The output of thesynchronization circuit 61 is provided to the cyclic prefix remover 62,which removes the cyclic prefixes inserted between each block of Nsamples. If the sampling frequency of the ADC is doubled, then everyother sample is chosen to form a block of N samples. The blocks of Nsamples are then serial-to-parallel converted using serial-to-parallelconverter 63. The parallel signals are input to a Discrete FourierTransform (DFT) stage 64, which converts the time domain samples back tothe frequency domain. Thus, the conversation completes thesynchronization and demodulation by the OFDM demodulators 22.

[0046]FIG. 6 is a block diagram illustrating synchronization processesthat may be conducted by the synchronization circuit 61. At least twosynchronization processes are provided: an open loop process; and aclosed loop process. The open loop process may be used in situationswhere the sampling frequency offset does not change too much with time,or the variations are slow as compared to the frame rate. The closedloop process may be used whenever the sampling frequency variations arefast as compared to the frame rate and it is possible that the optimaltiming instant may drift by an amount greater than a sample within aframe.

[0047] With respect to either the open loop or the closed loop process,the synchronization circuit 61 receives the signals that had beenconverted into discrete time samples by the ADC of the OFDM demodulator22 illustrated in FIG. 5. In the synchronization circuit 61, the signalsenter a time synchronization process 84. An exemplary timesynchronization process has been described in the commonly owned,pending patent application entitled: Time and Frequency Synchronizationin Multi-Input, Multi-Output (MIMO) Systems, which was filed in theUnited States Patent and Trademark Office on Apr. 24, 2002 and assignedSer. No. 10/128,821, and which is incorporated herein by reference.

[0048] After the time synchronization process 84, the discrete timesamples enter a Fast Fourier Transform (FFT) 86, which acts as ademodulator. After demodulation, the signal continues through the openloop process or the closed loop process.

[0049] In the open loop process, the signal is subjected to samplingfrequency offset estimation/phase rotation 90 and channel estimation 88,and the results are sent from the synchronization circuit 61 to thecyclic prefix remover 62 in the OFDM demodulator (as illustrated in FIG.5). Further details regarding the channel estimation 88 (also referredto as channel estimator) may be obtained from the commonly owned,copending patent application entitled: Estimating Channel Parameters inMulti-Input, Multi-Output (MIMO) Systems filed in the United StatesPatent and Trademark Office on Apr. 24, 2002 and assigned Ser. No.10/128,756, and which is incorporated herein by reference.

[0050] Exemplary equations relating to the actions of the open loopprocess are set forth below:

[0051] System Equation

R _(k,QxL) =Λ _(k,QxQ) ·S _(k,QxQ) ^(·η) _(kQxL) +W _(k,QxL)

[0052] R_(l,QXL)=Received demodulated sample matrix for the k'thsubcarrier,

[0053] S_(k,QXQ)=Transmit symbol matrix,

[0054] η_(k,QXL)=Channel coefficient matrix in the frequency domain,

[0055] Λ_(k,QXQ)=Diagonal matrix, (Λ_(k)qq)=exp {j2πβ(dQ+q)k(N+G)/N},

[0056] where

[0057] β=(T′−T)/T, is the sampling frequency offset and d is the runningindex of the number of Q blocks of OFDM symbols transmitted in theframe.

[0058] W_(l,QXL)=Matrix of AWGN samples with variance No/2 per dim.

[0059] The system equation relates to the received demodulated pilottone used to calibrate the system.

[0060] Open Loop Sampling Frequency Offset Estimation/Phase Rotation

[0061] OLI A. Sampling Frequency Offset Estimation $\begin{matrix}{{\hat{\beta}}_{k,{initial}} = \frac{{\angle \quad {{trace}\left\lbrack {R_{k}^{H\quad {previous}}R_{k}^{p,{current}}} \right\rbrack}} + {f_{k}\left( {{{pilot}\left( {d - 1} \right)},{{pilot}(d)}} \right)}}{2\quad \pi \quad {{{Qk}\left( {N + G} \right)}/N}}} \\{\quad {= \frac{{\angle \quad {\sum\limits_{l = 1}^{L}{{R_{l,l}}^{2}\quad {\exp \left( {j\quad 2\quad \pi \quad \beta \quad {{{Qk}\left( {N + G} \right)}/N}} \right)}}}} + {f_{k}\left( {{{pilot}\left( {d - 1} \right)},{{pilot}(d)}} \right)}}{2\quad \pi \quad {{{Qk}\left( {N + G} \right)}/N}}}} \\{\hat{\beta} = {\sum\limits_{k \in {pilots}}{w_{k}{\hat{\beta}}_{k,{initial}}}}}\end{matrix}$

[0062] where f_(k)(pilot(d−1),pilot(d))=π, if pilot(d−1) ≠pilot(d), else0, and W_(k) are the weights.

[0063]^(H) is the Hermitian operator equivalent to conjugate-transposeof a matrix. R_(k) ^(H,previous) is the received demodulated samplematrix at the k' th pilot tone for a block of Q OFDM symbols at therunning index (d−1). R_(k) ^(H,current) is the received demodulatedsample matrix at the k'th pilot tone for a block of Q OFDM symbols atthe running index d. The estimate {circumflex over (β)}_(d) may then bepassed through a low pass filter or a moving average filter to removesudden changes caused due to extraneous impediments such as noise. Amoving average filter may be represented by the following equation${\hat{\beta}}_{d} = {\frac{1}{M}{\sum\limits_{n = {d - M + 1}}^{d}{\hat{\beta}}_{n}}}$

[0064] where M is the length of the window. Larger the M more stable isthe estimate of β however slower is its response to any variations in β.The typical value of M may be chosen as QP/2 where P is the number ofblocks of Q OFDM symbols in the frame however it may be greater than ofless than that value.

[0065] OLI B. Phase Rotation

[0066] Once the estimate of the sampling frequency offset β is found, itis used to construct the sampling offset correction matrix Λ_(k) whichis then inverted and applied to the received sample matrix for all thesubcarriers R_(k) to obtain the new estimate of the received samplematrix R_(k) ^(new). $\begin{matrix}{{\hat{R}}_{k}^{new} = {\left( {\hat{\Lambda}}_{k}^{new} \right)^{- 1}R_{k}}} \\{{\hat{\Lambda}}_{k}^{new} = \begin{bmatrix}{\exp \left( {j\quad 2\quad \pi \quad k\quad {\hat{\beta}\left( {{dQ} + 1} \right)}\left( \frac{N + G}{N} \right)} \right)} & \quad & \quad & \quad \\\quad & {\exp \left( {j\quad 2\quad \pi \quad k{\hat{\beta}\left( {{dQ} + 2} \right)}\left( \frac{N + G}{N} \right)} \right)} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\\quad & \quad & \quad & {\exp \left( {j\quad 2\quad \pi \quad k{\hat{\beta}\left( {{dQ} + Q} \right)}\left( \frac{N + G}{N} \right)} \right)}\end{bmatrix}}\end{matrix}$

[0067] OLII. Open Loop Channel Estimation

[0068] Since sampling frequency was not accounted for at the time ofchannel estimation, improved channel estimates may be obtained asfollows

{circumflex over (η)}_(k) =B _(k) ^(H)(B _(k) B _(k) ^(H))⁻¹ R _(k)where B _(k)=Λ_(k) S _(k)

[0069] OLIII. Open Loop Tracking

[0070] Once the initial sampling frequency offset is done (Step OLI.)and channel estimates have been improved (Step OLII.), samplingfrequency offset may be tracked using

{circumflex over (Λ)}_(k) =R _(k) C _(k) ^(pH)(C _(k) ^(p) C _(k) ^(pH)+δI)⁻¹, δ→0 where C_(k) ^(p)=S_(k) ^(p)η_(k) ^(p) $\begin{matrix}{{{\hat{\beta}}_{k,{new}} = \frac{\angle \quad {\sum\limits_{q = 1}^{Q - 1}\left\lbrack {{\hat{\Lambda}}_{q,q,k}^{H\quad p}{\hat{\Lambda}}_{{q + 1},{q + {1k}}}^{p}} \right\rbrack}}{2\quad \pi \quad {{k\left( {N + G} \right)}/N}}},} & \quad & {{\hat{R}}_{k}^{new} = {\left( {\hat{\Lambda}}_{k}^{new} \right)^{- 1}R_{k}}}\end{matrix}$

[0071] The tracking of the sampling frequency offset may be eithercarried out using either Step OL I. or OLIII. or a combination of bothOLI and OL3.

[0072] Closed Loop Sampling Frequency Offset Estimation/Phase Rotation.

[0073] Advantageously, the closed loop process continually estimates,corrects and/or tracks the sampling frequency offset. The closed loopprocess includes actions undertaken by the sampling frequency offsetestimator/phase rotator 90, an error generator 96, and a loop filter andaccumulator 94. Exemplary equations relating to the actions are providedbelow:

[0074] CLI. Phase Rotation $\begin{matrix}{{\hat{R}}_{k}^{new} = {\left( {\hat{\Lambda}}_{k}^{new} \right)^{- 1}R_{k}}} \\{{\hat{\Lambda}}_{k}^{new} = \begin{bmatrix}{\exp \left( {j\quad 2\quad \pi \quad {{k/N} \cdot {{fraction}\left( {{err}_{1}(d)} \right)}}} \right)} & \quad & \quad & \quad \\\quad & {\exp \left( {j\quad 2\quad \pi \quad {{k/N} \cdot {{fraction}\left( {{err}_{2}(d)} \right)}}} \right)} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\\quad & \quad & \quad & {\exp \left( {j\quad 2\quad \pi \quad {{k/N} \cdot {{fraction}\left( {{err}_{3}(d)} \right)}}} \right)}\end{bmatrix}}\end{matrix}$

[0075] CLII. Error Generation $\begin{matrix}{\Omega_{k}^{early} = {\Lambda_{k}^{- \zeta}S_{k}^{p}\eta_{k}^{p}}} \\{\Omega_{k}^{late} = {\Lambda_{k}^{+ \zeta}S_{k}^{p}\eta_{k}^{p}}} \\{\Omega_{k}^{early} = \begin{bmatrix}{\exp \left( {{- j}\quad 2\quad \pi \quad k\quad {\zeta/N}} \right)} & \quad & \quad & \quad \\\quad & {\exp \left( {{- j}\quad 2\quad \pi \quad k\quad {\zeta/N}} \right)} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\\quad & \quad & \quad & {\exp \left( {{- j}\quad 2\quad \pi \quad k\quad {\zeta/N}} \right)}\end{bmatrix}} \\{\Omega_{k}^{early} = \begin{bmatrix}{\exp \left( {j\quad 2\quad \pi \quad k\quad {\zeta/N}} \right)} & \quad & \quad & \quad \\\quad & {\exp \left( {j\quad 2\quad \pi \quad k\quad {\zeta/N}} \right)} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\\quad & \quad & \quad & {\exp \left( {j\quad 2\quad \pi \quad k\quad {\zeta/N}} \right)}\end{bmatrix}}\end{matrix}$

[0076] Let

C _(k) ^(early) ={circumflex over (R)} _(k) ^(early)Ω_(k)^(early H)(Ω_(k) ^(early)Ω_(k) ^(early H))⁻¹

C _(k) ^(early) ={circumflex over (R)} _(k) ^(new) Ω _(k)^(late H)(Ω_(k) ^(late) Ω _(k) ^(late H))

[0077] Let $\begin{matrix}{\Xi_{q}^{early} = {\sum\limits_{k \in {pilots}}C_{q,q,k}^{early}}} & {{q = 1},{\ldots \quad Q}} \\{\Xi_{q}^{late} = {\sum\limits_{k \in {pilots}}C_{q,q,k}^{late}}} & {{q = 1},{\ldots \quad Q}}\end{matrix}$

[0078] The instantaneous error signal is generated from the early andlate outputs as

α_(q)(d,ε)=|Ξ_(q) ^(early)|²−|Ξ_(Q) ^(late)|²

[0079] CLIII. Low Pass Filtering and Error Accumulation

[0080] The instantaneous error is passed through a low pass filter. Lowpass filter may be a simple first order low pass filter of the type

b(d, ε)=a·a(d, c)+(1−a)a(d−1, ε)

[0081] where α is the forgetting factor or it can be a more complexfilter based on any of the filter design techniques. The low pass filtermay also be a moving average filter as discussed or any filter designedusing certain specific design criteria.

[0082] The output of the low pass filter is then accumulated as${{err}(n)} = {\sum\limits_{d = 1}^{n}{b\left( {d,ɛ} \right)}}$

[0083] Finally, the error is separated into its integer (interger(err))and fractional (fraction(err)) components and sent to the timingsynchronization and phase rotation circuits respectively.

[0084] In one possible embodiment, a non-coherent early-late PhaseLocked Loop (PLL) is used for error generation. The PLL in the closedloop mode requires that the initial time synchronization be accurate toone-half of the sampling time T. This is already achieved since thesampling frequency is doubled at the front end of the receiver.

[0085] Also, it is found that doubling the sampling frequency for theopen loop estimation improves the system performance tremendously andthe system is able to provide a similar performance for a frame sizelarger by a factor ten times or more.

[0086] The Loop Filter and Accumulator 94 incorporates a low pass filterand the output of the filter is used to obtain the filtered estimate ofthe Sampling Frequency Offset, which is used to calculate a correctionsignal to be added to the system at the Time Synchronization stage 84.In other words, the output of the low-pass filter is accumulated overthe time period of the frame. It is then broken into integer andfractional components to be sent back to the phase rotation block and tothe time synchronization circuit for synchronization instant adjustment.

[0087] The sampling frequency offset detection, estimation and controlsystem may be used in either open loop or a closed loop mode as thesystem design sees fit.

[0088] It should be emphasized that the above-described embodiments ofthe present invention are merely possible examples of implementations,merely set forth for a clear understanding of the principles of theinventions. Many variations and modifications may be made to theabove-described embodiments of the inventions without departingsubstantially from the principles of the inventions. All suchmodifications and variations are intended to be included herein withinthe scope of this disclosure and protected by the following claims.

We claim:
 1. A method for detection of sampling frequency offset andcorrection of the sampling frequency offset, comprising: causing amatrix of pilot tones to be inserted into data prior to transmission ofthe data; and causing a receiver receiving the data to pass the datathrough a synchronization circuit for detecting the sampling frequencyoffset by reference to the matrix of pilot tones in the data and forcorrecting the sampling frequency offset.